Bayesian Model Averaging is not built into EViews, but it depends what you want to do. Do you just want point estimates of forecasts, or do you need entire distributions? Have you already calculated the model probabilities?

EViews isn't going to directly calculate the model probabilities. But you can use the Schwarz criterion to compute a reasonable large sample approximation for the posterior model odds. Then you multiply the forecast from each model by the model probability.

My favorite reference for this sort of stuff is Bayesian Econometrics, by Gary Koop.